Any non-credible threat that is part of a Nash equilibrium in a sequential game cannot be played along the Nash equilibrium path.

Question

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In a Nash equilibrium, each player's strategy is optimal given their opponent's strategies. If a player's threat is not credible, it means that they will not follow through with the threat if their opponent chooses a strategy that deviates from the Nash equilibrium. If this threat is not credible, the opponent will not believe it and will not be deterred from deviating from the Nash equilibrium. Therefore, the threat cannot be part of the Nash equilibrium path, where players are playing their optimal strategies given the opponent's strategies.

Any Non-Credible Threat That Is Part of a Nash Equilibrium